Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
272 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 18. #3946 | C4 | semidirect |
| 19. C8×Dic5 | C4 | semidirect |
| 73. #168 | C4⋊C4 | semidirect |
| 99. Dic5 | #97 | semidirect |
| 150. C5 | #1770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3947 | 2 |
| C2×#3946 | 2 |
| C2×C8×Dic5 | 2 |
| C4×#683 | 2 |
| C2×#3935 | 2 |
| C5×#336 | 2 |
| #64770 | 2 |
| #1770 | 5 |